Circuit Considerations

Electromagnetic stimulation devices in general are based on a capacitor driving current into the inductance of the stimulator core. A full circuit and a simplified circuit are presented in Figure 3.

Figure 3

(Full circuit)

(Simplified circuit)

The dc charged capacitor is allowed to resonate a complete cycle, and the core head is where inductance is generated. In a situation without winding resistance, the capacitive energy would shift to inductive energy , and reverse back to the capacitor. The period of time required for a full wavelength can be expressed by .

The inductor core generates a magnetic flux that passes into the biological tissue (i.e. the cortex, in the case of TMS) and induces a voltage through the tissue linked by the flux. Only a fraction of that flux will connect a circuit consisting of the intracellular and extracellular space of a nerve through the membrane wall because the induced voltage is only a fraction of the flux linking the iron core winding. The circuit of the nerve targeted by the magnetic stimulator is shown below in Figure 4.

Figure 4

During the resting state, the cell membrane is low in permeability (i.e. mobility) to ion flow (mainly Na+). The following model focuses on a subthreshold state over a long nerve length, where capacitance of the membrane wall is expressed in terms of permittivity ε for a per unit axial length , radius r, and thickness ∆.

Membrane resistance Rm is expressed in terms of membrane thickness and membrane wall conductance, σm.

And intracellular resistance, Ri, per unit length can be written in terms of intracellular conductivity, σi, and is significantly greater than the extracellular resistance, which is very small as a result of the extracellular space being very large.

Kent Davey and Epstein C.M.. Magnetic Stimulation Coil and Circuit Design. IEEE Transactions On Biomedical Engineering, Vol. 47, No. 11, November 2000